484 
NATURE 
[April 20, 1871 

these solids they knew little, the theory of the sphere alone 
appears developed to a certain degree necessary for astro- 
nomical purposes. Of proportions and similar figures 
they knew nothing. 
The succeeding chapters relate to Geometry in Greece. 
We shall only mention a few of the most striking differ- 
ences between Prof. Bretschneider and his predecessors. 
That most of the anecdotes about Pythagoras—his long 
captivity in Babylon, for instance,—are rejected, need 
scarcely be mentioned. But many readers will be sur- 
prised to hear that Plato is not considered a very eminent 
mathematician as he himself did almost nothing to enrich 
this science, and most of the theorems usually believed to 
be due to Plato are his pupils’. Thus the conic sections 
were invented by Menaichmos. Again, the veductio ad 
absurdum is considered one of the simplest methods of 
demonstration and used long before Euclid thought of it. 
One of the most important points in the book consists 
in along passage out of Eudemos’ “ History of Mathe- 
matics” (about 340 B.C.), which Bretschneider was fortu- 
nate enough to discover in the commentary on Aristotle by 
Simplikios. It contains a critique on investigations on 
tie problem of squaring the circle. Some of the methods 
here employed are exceedingly interesting, as they show 
what means were at the disposal of the mathematician. 
Antiphon, a contemporary of Socrates, inscribes a regular 
polygon in a circle, and then proceeds in the well-known 
manner to double the number of sides till these at last 
coincide with the circumference of the circle. He then 
considers the circle as a regular polygon, and says that it 
may be converted, like any other polygon, into a square. 
It appears, therefore, that Antiphon was the first who in- 
troduced infinitesimals into geometry, and thus became the 
forerunner of Archimedes. These methods were, however, 
far too much in advance of his time, and Eudemos re- 
jects them as not exact. Hippocrates, known by his 
quadrature of the lunulze, makes several attempts to ex- 
tend this discovery, and to obtain similar results for 
other lunulz and thence for the whole circle. Some of 
these attempts indicate great power, although they lead 
to nothing tangible. 
The book contains many other important results, and 
all those who take an interest in the history of the de- 
velopment of science will feel indebted to the author for 
its publication, 


OUR BOOK SHELF 
Notes on the Natural History of the Strait of Magellan 
and West Coast of Patagonia, made during the Voyage 
of H.M.S. “ Nassau,” in the years 1866—1869. By 
Robert O. Cunningham, M.D., F.Z.S., &c., Naturalist to 
the Expedition. (Edinburgh: Edmonston and Douglas.) 
WE regret to be obliged to find fault with the work of 
a naturalist, but duty to our readers compels us to say 
that this book should never have been published. There is 
perhaps no part of the world which is at once so remote 
and inhabited by such interesting savage tribes, with the 
main features of whose scenery and natural productions 
the public is so well informed as that which forms the 
subject of this book. It is therefore surprising that a 
gentleman who has had the opportunity of studying the 
natural history of this region at his leisure, shotld have 
thought himself justified in printing a volume of 500 pages 

of his rough journal, nine-tenths of which are occupied 
with a bald record of the usual monotonous incidents of 
sea and shore excursions, and with repetitions of facts 
already given us by Darwin, Hooker, and a host of other 
less eminent writers. There are, of course, some interesting 
facts and some original observations in this volume, but 
they are so thinly scattered amid a mass of details of 
weather and personal incidents, with records of the 
gathering of every common plant and the capture 
of every common as well as uncommon bird or in- 
sect, asto be not worth the search after. The book too 
is got up with an utter disregard of the reader’s con- 
venience. The author journalises his whole voyage, and 
at least one third of the volume treats of other parts of 
the world than those indicated by the title, yet the heading 
throughout is “Strait of Magellan,” even when Rio 
Janeiro, Valparaiso, or the Azores are beinz described. 
Neither is there any indication of years or months, ex- 
cept when a change occurs ; and if we find that some- 
thing was captured on the “ 14th,” we have to go back or 
forward many pages to discover whether we are in May 
or December. The plates too are wholly without refer- 
ences to the letterpress ; and we find a curious plant 
(Philesia buxifolia) described at page 173, and figured at 
page 321, with no reference from description to figure or 
from figure to description. The illustrations seem thrown 
in at random, anything the author collected being appa- 
rently deemed worthy of a plate. On no other principle 
can we explain the plate devoted to an indifferent figure of 
the cranium of so commonan animal as the puma ; and 
another to the furcula of a condor, the picking-up of 
which is recorded at page 113, and figured full size, 
@ propos of nothing, at page 303. 
It is the more to be regretted that such a book as this 
has been published, because there is ample room for one of 
a different character, and for which Dr. Cunningham must 
have collected or have been able to obtain ample materials. 
The temperate parts of South America form a well-marked 
district, the productions of which are exceedingly inte- 
resting and their affinities well worthy of careful study. 
The relations of the fauna and flora of this district to 
those of Tropical America, of Europe, of Australia, and 
of New Zealand, require a thorough and critical examina- 
tion; and this could hardly fail to throw much light on 
the means by which organic forms have been distributed, 
and on the relative importance of the various zoological 
regions into which the globe has been divided. 
The author states in his preface that he has not yet 
completed the examination of his materials. Why then 
did he rush into print before he was able to lay before the 
world a single generalised result of his three years’ 
voyage ? W. 
Les Houilléres en 1869. Par Amédée Burat, Secrétaire 
du Comité des Houilléres Frangaises. Texte et Atlas. 
(Paris, 1870. London: Williams and Norgate.) 
THIS is an annual publication of a semi-official character, 
proceeding from M. Burat, the Secretary of the very useful 
Association of Coal-mine Proprietors in France. We are 
not aware that any such committee of coal owners exists in 
Great Britain, although other trades or professions, such as 
bankers, railway companies, &c., have similar committees. 
The Iron and Steel Institute, which has lately been holding 
its meeting in London, fulfils to some extent this purpose in 
regard to the iron trade. Wherever such associations 
exist we wish that they could be persuaded to publish as 
complete and valuable reports on the condition of their 
branch of trade as we have in these annuai reports on the 
French coal trade, now available for ten or eleven years 
back. The present report consists of four chapters, which 
treat respectively of the strikes of the coal-miners, which 
had greatly interfered with the trade, improvements in 
the machinery and modes of working coal mines, the 
statistical conditions of the production of coal in 1860, 
